Cyan comments on Harry Potter and the Methods of Rationality discussion thread - Less Wrong
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I believe it was a method of predicting the future using math (such as adding values of letters of people's names).
That's what it's supposed to be in reality, but as a subject at Hogwart's, that's far from clear.
ETA: Maybe my use of the phrase "this universe" was ambiguous? I meant the fic universe, not the universe I'm currently existing in.
In an interview, JKR confirmed that arithmancy at Hogwarts is as it is in real life. Only I would imagine that it actually works - otherwise there would be no basis to Hermione's claim that it's more robust and trustworthy than divination.
Awesome. Thanks!